Problem #3: Consider the set C'([a, b]), the set of differentiable functions (that is, we take the set of all functions f : [a, b] → R so that f' is well defined). Show that this set forms a vector space over R. [This means you must explain why: 1) the sum f + f,g in this set is still in the set, and 2) the scalar multiple cf of any function f in this set is still in the set, for any c in R and 3) the function f(x) = 0 is in the set. You may find it helpful to use properties of derivatives that you studied once upon a time in calculus!] of two functions

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Q: Please solve this old vector calculus problem by shpwing all the steps. Thanks!

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